The CCRM is basically a purpose built set of relays. They usually power their devices or not. I would be hard pressed to think of a failure more where the CCRM could "cause" the symptoms that you are reporting.
Next issue. What model year Mustang are we dealing with anyway? Is this a 1996-1998 return style or a 1999-2004 return-less? But the fuel pressure of 32 PSI at idle is exactly as it should be. But in order to correctly trouble shoot this issue we need to know what the fuel pressure is when the problem is occurring. This is where the 1999-2004 has a real advantage as it's possible to use an ODB2 scanner to monitor FRPS.
Do you have an ODB2 scanner? If you did this might give access to PCM operating PID's that might make short work of your problem. Here's some information on an affordable Windows based unit.
ForScan ODB2 scanner w ELM327 USB
While working on your car have you ever wanted: to find an ODB2 operational PID value (say fuel pressure or MAF)? How about graph a PID value over time? Or compare multiple PID's over time? Access a bi-directional PCM control such as test a...
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Recommendation. Make the next trouble shooting step a through review of the battery and alternator.
Howto perform charging system voltage drop test
To anyone else reading any of my posts I usually include the line: Today's cars simply will not run right without a strong battery and charging system! Cut corners here at your own risk I'm a big believer in starting with the basics. As such I...
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If this is a return style fuel system it would be helpful to use an external fuel pressure gauge in such a way as it's visible while driving. An option would be to monitor long term fuel trims (LTFT) while the problem is occurring. IF the fuel pressure drops during heavy load, this will show up as the PCM adding fuel to the STFT and LTFT.
If the STFT and LTFT show a "lean" condition also consider that clogged fuel injectors could be playing a role. Consider an injector cleaning and flow test service such as InjectorRX.com. Once cleaned and tested they are as good as new (but cheaper).